Dynamics

1.) What is Dynamics?

In physics, dynamics is the study of forces (why objects move). When studying dynamics, vectors are used to describe forces. Vectors are often identified with arrows. The longer the vector is, the stronger the force is.http://en.wikipedia.org/wiki/Dynamics_(physics)

2.) Force vs. Acceleration Lab

We did an experiment in class to determine the relationship between force and acceleration. We put a car with a weight and a force-measurer on a track, with a sonic ranger at the end, and plugged in everything, including our LabPro, to our computer. We took two sets of data, one with a 200 g mass on top of the car and another with a 1 kg mass on top of the car. We collected data in LoggerPro while pushing and pulling the car along the track with the hook coming out of the force-measurer. Our data points in the graph of force vs. acceleration were all connected, so we double clicked on the graph, unchecked the boxed labeled “connect points”, and checked the box labeled “point protectors”. This made the graph into just points instead of lines.

3.) Forces and Types of Forces

A force is a push or pull, measured in newtons. Forces cause acceleration, NOT motion.
Force is a vector quantity, meaning that it is made up of a magnitude and a direction

There are two types of forces:

1. Contact Force- You cannot touch something without it touching you. When you touch an object you come into physical contact with the object. Because you are in physical contact with another object a force arises on the object you are touching. Forces come in pairs, so in return the object you are in physical contact with applies an equal force on you in return. Examples: Hand on Table, leaning on a wall, running on a track.

In the diagram above the gravitational forces pulling planets towards the sun is illistrated. This is an example of an action at a distance force becasue although the planets never come in physical contact with the sun their is still a force being exchanged between them.

A runner running on a track is an example of a contact force because the feet of the runner touch the ground (physical contact). The feet push down on the track, and the track pushes up on the feet.

4.) Inertia: Newton's 1st Law

Next, we learned Newton's First Law of Motion. It states that if the force acting on an object is zero, then the acceleration of the object is zero and its velocity is constant. This results that an object that is not moving will not move until a force acts upon it, and an object that is moving will not change its velocity until an outside force acts upon it. Forces do not cause all types of motion, only acceleration (force is not required to keep an object moving).

This picture is an example of Newton's First and Second Laws of Motion. The first two picture show his second law while the third picture shows his third. In the last picture, it is shown that the marble will continue to roll on the flat horizontal surface without stopping until acted on by an outside force. Theoretically, if an outside force never acted on the marble, the marble would roll forever

5.) F=ma: Newton's 2nd Law

The rate at which an object is accelerating depends on how hard it is hit, pushed, or pulled and the mass of the object. The acceleration of an object is proportional to the force acting upon it.

After we got the graphs in the force vs. acceleration experiment, we clicked the f(x) button and did the linear option because this graph looked like a line to us. It worked, so we thought we could use the equation y = mx +b from which to derive our equation.
Y : F (force, measured in Newtons, on the y axis)
M : m (mass, slope of the line)
X : a (acceleration, on the x axis)
B : F0 (however, there is no such thing as initial force, and there are many forces acting the object)

Therefore, our new equation is F = ma. Also, we put a sigma (Σ) in front of the F. Sigma is the Greek letter for the sum (in math), so when we put this in front of the F, we are referring to total force, or the sum of all the forces. We also put a vector symbol on top of the F and the a, meaning that these are vector quantities. In LoggerPro, the units for the slope are shown as N/m/s^2. We knew that slope equals mass because 1. slope was constant on our graph, and mass was the only constant in our equation, and 2. by substituting units in for their unknowns, we found N=kg*m/s^2. Then we rearranged this equation to solve for kg (because kg is the units for mass) and came up with kg=N/m/s^2. N/m/s^2 was the same units of slope that Logger Pro gave us, proving mass to be slope.
By substituting the variables, we also found that N = kg * m/s^2.

6.) Newton's 3rd Law

Newton's third law states that for every force there is an equal and opposite force, or in other words you cannot touch and object without being touched back. This law tells us that forces come in pairs (action force and reaction force). It also says that forces that come in pairs are equal in magnitude, but opposite in direction.The swimmer is applying a force on the wall, but her motion indicates that a force is being applied on her too. This force comes from the wall, and it's equal in magnitude and opposite in direction.

For example, if a girl were to lead on a wall, the wall would push back on her with the same force. From this, a common question is asked. If everything being pushed gets pushed back with the same force, then how does anything move? This happens because there are other forces that act on the object. These forces either give the object more force which makes it unable to move or gives the other force more force making the object move.

7.) Mass vs. Weight

Click Here for a helpful link regarding mass vs. weight
Mass is the measure of how much matter (or stuff) something is made of, and is usually measured in kilograms. Weight, on the other hand, measures the force of gravity acting on an object, and is measured in Newtons (N). Weight depends on location (because of gravity) and it is a vector quantity. In simple terms, mass is stuff and weight is force.
So on the moon, your mass would not change from that on Earth unless you added or subtracted something from your body matter on the way. Weight, on the other hand, would change, because the force of gravity on the moon is less than that of earth (about 1/6 of that on earth).
Weight (or the force of gravity, Fg) = mass*accelerationMass is also a measure of an objects inertia. Intertia is the tendancy of an object to continue what it is already doing, therefore the more mass an object has the more inertia it has as well.

8.) Vectors

A vector is a quantity that has both a magnitude and a direction. We can draw/graph vectors by drawing arrows. The length of the arrow shows the magnitude of the quantity, and the direction of the arrow shows the direction of the quantity. By adding 2 vectors, we can find the displacement, or "resultant vector", of our quantity. So let's say you have two vectors, vector A, and vector B. To find their sum:

1. Line them up head to tail.
2. Draw another arrow starting at tail of arrow A and going to the head of arrow B.
The green arrow shows the displacement, or resultant vector, of vector A and B.

9.) Free Body Diagrams

Free Body Diagrams are basically pictures to show the different forces acting on an object. Some forces to consider when drawing an FBD are...

Force of Gravity- always pointing in a downward direction

Force of Air Resistance- this is a friction force

Force of Friction- there is always friction when two objects are touching

Force of Tension- this is always through some physical thing (sting, cable, chain, etc,) attached to an object. The force will always be pulling the object in the opposite direction of the applied force. For example, if you applied a force onto a cable, trying to pull it down, the applied force would be acting downwards, and the tension force would be acting upwards.

Normal Force- when an object is resting on a plane, the Normal Force will be perpendicular to the plane that the first object is resting on. Because of Normal Forces, you don't fall through the chair you are sitting on.

Click Herefor a helpful link regarding Free Body Diagrams.
When drawing free body diagrams, always remember to start the force from the center of the object, as shown below.

The picture above is an example of a free body diagram, illustrating an object positioned on a slope. The normal force pushes up parallel to the surface (NOT always opposite the direction of the force of gravity), the force of gravity points straight down (no matter if the object is moving, on a slope, at rest, etc.), and the force of friction pushes back on the box as it slides down the incline.Click here for more information about forces on inclined planes.

10.) Hooke's Law

Hooke’s law of elasticity, developed by Robert Hooke, is an approximation that an extension of a spring is proportional with the loaded added to it and long as the load is equal and does not surpass the elastic limit.

Mathematically, Hooke's law states that

x is the displacement of the end of the spring from its equilibrium(balance) position (or the stretch length).

F is the force applied to the object.

k is the spring constant, or "stiffness" of the spring. The larger the value of "k" is, the more stiff the spring is, and the smaller the value of "k" is, the stretchier the spring is.

There is a negative sign on the right had side of the equal sign because the force on the object (usually the tension force) always acts in the opposite direction of the stretch length (x). For example, when a spring is stretched to the left, the actual spring pulls back to the right. (In this example, the tension force on the spring is pulling it back to the right, while the strech length is in the direction it is moving, left.)

This law was named after the 17th century British physicist, Robert Hooke. He states this law in Latin as “Ut tensio, sic vis”, meaning, "As the extension, so the force".

The term, elastic, is used to describe an object that follows Hooke's Law like springs. Likewise, inelastic is used to describe an object that does not obey Hooke's Law, for example, rubber bands. When something does not follow Hooke's Law, it forms a hysterisis loop when graphed. This area on the graph between the stretching and unstretching energeies, is the energy that is lost when a rubber band is stretched. This energy is lost to heat, so when the rubber band is unstretched, it does not unstretch in the same way since it lost energy to heat energy.

A spring is an example of an elastic object because it follows Hooke's Law.